Observable Lower Bounds to Quantum Information

Entanglement is a fundamental property of quantum mechanics and plays a central role in quantum information science, quantum computation, and many-body physics. It represents non-classical correlations between subsystems that cannot be explained by local hidden variables. Despite its conceptual importance, entanglement remains difficult to quantify in practice because it is not directly observable. Various tools have been developed to estimate entanglement. Among these, a particularly insightful approach is based on the concept of squashed entanglement, a rigorous entanglement measure defined through the quantum conditional mutual information. Specifically, the squashed entanglement of a bipartite state is given by the infimum of the conditional mutual information over all possible extensions. This measure is of strong theoretical interest because it connects entanglement with information-theoretic quantities, and thus with entropy. However, it poses significant challenges for practical computation, as it typically requires complete knowledge of the global quantum state, which is experimentally inaccessible in most settings. This work addresses that challenge by deriving experimentally accessible lower bounds on the conditional mutual information in many-body quantum systems. Through numerical analysis, we validate the effectiveness of these bounds in several nontrivial scenarios, highlighting their utility not only for entanglement quantification, but also for a wide range of tasks crucial to the effective characterization of components in quantum computing.